Why we can only constant expressions in c switch statements? 2. Why remaining cases executed when no Break used in switch?

In C Switch statements

1. Why only constant expressions
2. Why all remaining cases are executed after no break is used?

" : "

A switch is expected to be translatable into a range-checked jump through a jump table.

For something like*:

void sw(unsigned X){ 
	switch(X){ 
	case 0: case0(); 
	case 1: case1(); 
	case 2: case2(); 
	case 3: case3(); 
	case 4: case4(); 
	case 5: case5(); 
	} 
}

You can expect codegen equivalent to (expressed via the GNU labels-as-values C extension¸ which just reflects a basic assembler capability):

void sw0(unsigned X){
	static const void *table[]={
        //store label addresses
		&&case0,
		&&case1,
		&&case2,
		&&case3,
		&&case4,
		&&case5,
	};
	if(X<=5){
		goto *table[X];
        
        //the code with the labels:
		case0: case0();
		case1: case1();
		case2: case2();
		case3: case3();
		case4: case4();
		case5: case5();
	}
}

(Indeed, clang generates exactly the same code for the two functions: https://gcc.godbolt.org/z/nfvz9sGxM)

1. The case labels need to be constants because they are to become positions in the static case table (possibly after some adjustments). It wouldn't be possible to define a static table based on dynamic positions.

2. Fall-through is automatic because that's what you get with C/assembly code (whether it has labels or not): one statement/instruction is executed after another unless a jump is made.

You might notice that the C standard refers to "cases" as case labels and that's what they are. They're just labels (i.e., they mark a position/address in code) with some added restrictions/expectations:
they can only be inside switches and their value (the address of the label) is expected to be stored in the nearest enclosing switch's jump table (if that particular switch is indeed compiled into one--there are other options).

*Example taken from my Quora answer to How do C compilers produce machine code for switch statements and cases, which also mentions what other codegen you might get with switch's besides straightforward jumptables.